On diagonally structured problems in unconstrained optimization using an inexact super Halley method

We consider solving the unconstrained minimization problem using an iterative method derived from the third order super Halley method. Each iteration of the super Halley method requires the solution of two linear systems of equations. We show a practical implementation using an iterative method to solve the linear systems. This paper introduces an array of arrays (jagged) data structure for storing the second and third derivative of a multivariate function and suitable termination criteria for the (inner) iterative method to achieve a cubic rate of convergence. Using a jagged compressed diagonal storage of the Hessian matrices and for the tensor, numerical results show that storing the diagonals are more efficient than the row or column oriented approach when we use an iterative method for solving the linear systems of equations.     

Tetrasubstituted phenanthrolines as highly potent, water-soluble, and selective g-quadruplex ligands

Small molecules capable of stabilizing the G-quadruplex (G4) structure are of interest for the development of improved anticancer drugs. Novel 4,7-diamino-substituted 1,10-phenanthroline-2,9-dicarboxamides that represent hybrid structures of known phenanthroline-based ligands have been designed. An efficient synthetic route to the compounds has been developed and their interactions with various G4 sequences have been evaluated by F?rster resonance energy transfer (FRET) melting assays, fluorescent intercalator displacement (FID), electrospray ionization mass spectrometry (ESI-MS), and circular dichroism (CD) spectroscopy. The preferred compounds have high aqueous solubility and are strong and potent G4 binders with a high selectivity over duplex DNA; thus, they represent a significant improvement over the lead compounds. Two of the compounds are inhibitors of HeLa and HT1080 cell proliferation.     

Multi-elemental bio-imaging of rat tissue from a study investigating the bioavailability of bismuth from shotgun pellets

In recent years, bismuth has been promoted as a "green element" and is used as a substitute for the toxic lead in ammunition and other applications. However, the bioavailability and toxicity of bismuth is still not very well described. Following a hunting accident with bismuth-containing shots, a bioavailability study of bismuth from metal pellets inoculated into rat limb muscles was carried out. Bismuth could be found in urine and blood of the animals. Bio-imaging using laser ablation ICP-MS of thin sections of the tissue around the metal implant was carried out to find out more about the distribution of the metal diffusing into the tissue. Two laser ablation systems with different ablation cell designs were compared regarding their analytical performance. Low concentrations of bismuth showing a non-symmetrical pattern were detected in the tissue surrounding the metal implant. This was partly an artefact from cutting the thin sections but also bio-mobilisation of the metals of the implant could be seen. An accumulation of zinc around the implant was interpreted as a marker of inflammation. Challenges regarding sample preparation for laser ablation and bio-imaging of samples of diverse composition became apparent during the analysis.     

Structure and stability of networked metallofullerenes of the transition metals

A DFT investigation of substitutionally doped fullerenes MC59 of second- and third-row transition metals shows that their stability increases toward the right-hand side of the d-block. Whereas the structural deviation from that of C60 depends on the size of the metal atom, stability is governed by electronic properties of the transition metal atom. A range of MC59 compounds of group 6-8 metals are predicted to have sufficient stability for experimental observation.     

Time discretization of an evolution equation via Laplace transforms

Following earlier work by Sheen, Sloan, and Thomée concerningparabolic equations we study the discretization in time of aVolterra type integro-differential equation in which the integraloperator is a convolution of a weakly singular function andan elliptic differential operator in space. The time discretizationis accomplished by using a modified Laplace transform in timeto represent the solution as an integral along a smooth curveextending into the left half of the complex plane, which isthen evaluated by quadrature. This reduces the problem to afinite set of elliptic equations with complex coefficients,which may be solved in parallel. Stability and error boundsof high order are derived for two different choices of the quadraturerule. The method is combined with finite-element discretizationin the spatial variables.     

Stereoselective total synthesis of ieodomycin C

A concise stereoselective synthesis of the marine natural product ieodomycin C (3) has been achieved from commercially available pyridinium-1-sulfonate (8) in eight linear steps and 14% overall yield. The key synthetic steps included a B-alkyl Suzuki–Miyaura cross-coupling reaction and an Evans–Nagao acetate aldol reaction. The same synthetic sequence was used for preparing the enantiomer of ieodomycin C (3). Our efforts confirmed the structure of the antibacterial natural product 3.     

Syntheses of Some Sulfur‐Containing Polyunsaturated Fatty Acids as Potential Lipoxygenase Inhibitors

Starting from (all‐Z)‐eicosa‐5,8,11,14,17‐pentaenoic acid (EPA) and (all‐Z)‐4,7,10,13,16,19‐docosahexaenoic acid (DHA), several polyunsaturated fatty acids, containing a sulfur atom either in the chain or in a thiophene ring, have been synthesized as potential inhibitors of lipoxygenases.     

A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis

We introduce a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression of limestones under the attack of SO₂, in high permeability regime. By means of a dimensional scaling, the qualitative behavior of the solutions in the fast reaction limit is investigated. Explicit asymptotic conditions for the front formation are derived.